Principles of Flight

PRINCIPLES OF FLIGHT

ATPL GROUND TRAINING SERIES

I Introduction I Introduction

© CAE Oxford Aviation Academy (UK) Limited 2014
All Rights Reserved

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This text book has been written and published as a reference work to assist students enrolled on an approved
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examinations. Nothing in the content of this book is to be interpreted as constituting instruction or advice
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IIntroduction Introduction I

iii

I Introduction

I Introduction Textbook Series

Book Title Subject

1 010 Air Law

2 020 Aircraft General Knowledge 1 Airframes & Systems

Fuselage, Wings & Stabilising Surfaces
Landing Gear
Flight Controls
Hydraulics
Air Systems & Air Conditioning
Anti-icing & De-icing
Fuel Systems
Emergency Equipment

3 020 Aircraft General Knowledge 2 Electrics – Electronics

Direct Current
Alternating Current

4 020 Aircraft General Knowledge 3 Powerplant

Piston Engines
Gas Turbines

5 020 Aircraft General Knowledge 4 Instrumentation

Flight Instruments
Warning & Recording
Automatic Flight Control
Power Plant & System Monitoring Instruments

6 030 Flight Performance & Planning 1 Mass & Balance

Performance

7 030 Flight Performance & Planning 2 Flight Planning & Monitoring

8 040 Human Performance & Limitations

9 050 Meteorology

10 060 Navigation 1 General Navigation

11 060 Navigation 2 Radio Navigation

12 070 Operational Procedures

13 080 Principles of Flight

14 090 Communications VFR Communications
IFR Communications

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IIntroduction Introduction I

Contents

ATPL Book 13 Principles of Flight

1. Overview and Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2. The Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23
3. Basic Aerodynamic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4. Subsonic Airflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5. Lift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6. Drag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7. Stalling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
8. High Lift Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
9. Airframe Contamination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
10. Stability and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
11. Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331
12. Flight Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
13. High Speed Flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
14. Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
15. Windshear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
16. Propellers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
17. Revision Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
18. Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

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I Introduction I Introduction

vi

1Chapter

Overview and Definitions

Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
General Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Greek Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Self-assessment Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1

1 Overview and Definitions 1 Overview and Definitions

Figure 1.1

2

1Overview and Definitions Overview and Definitions 1

Overview

The primary requirements of an aircraft are as follows:
• a wing to generate a lift force;
• a fuselage to house the payload;
• tail surfaces to add stability;
• control surfaces to change the direction of flight; and
• engines to make it go forward.
The process of lift generation is fairly straightforward and easy to understand. Over the
years aircraft designers, aerodynamicists and structural engineers have refined the basics
and, by subtle changes of shape and configuration, have made maximum use of the current
understanding of the physical properties of air to produce aircraft best suited to a particular
role.
Aircraft come in different shapes and sizes, each usually designed for a specific task. All aircraft
share certain features, but to obtain the performance required by the operator, the designer
will configure each type of aeroplane in a specific way.
As can be seen from the illustrations on the facing page, the position of the features shared
by all types of aircraft i.e. wings, fuselage, tail surfaces and engines varies from type to type.

Why are wing plan shapes different?
Why are wings mounted sometimes on top of the fuselage instead of the bottom?
Why are wings mounted in that position and at that angle?
Why is the horizontal stabilizer mounted sometimes high on top of the fin rather than on
either side of the rear fuselage?
Every feature has a purpose and is never included merely for reasons of style.

3

1 Overview and Definitions 1 Overview and Definitions

An aeroplane, like all bodies, has mass. With the aircraft stationary on the ground it has only
the force due to the acceleration of gravity acting upon it. This force, its WEIGHT, acts vertically
downward at all times.

W

Figure 1.2 The force of weight

Figure 1.1 The Force of Weight
Before an aeroplane can leave the ground and fly, the force of weight must be balanced by a
force which acts upwards. This force is called LIFT. The lift force must be increased until it is the
same as the aeroplane’s weight.

L

W

Figure 1.3 The forces of weight & lift

Figure 1.2 The Forces of Weight and Lift

4

1Overview and Definitions Overview and Definitions 1

To generate a lift force, the aeroplane must be propelled forward through the air by a force
called THRUST, provided by the engine(s).

L

W

Figure 1.4 The forces of weight, lift & thrust

From the very moment the aeroplane begins to move, air resists its forward motion with a
force called DRAG.

L

W

Figure 1.5 The forces of weight, lift, thrust & drag

Figure 1.4 The Forces of Weight, Lift,
Thrust and Drag

5

1 Overview and Definitions 1 Overview and Definitions

When an aeroplane is moving there are four main forces acting upon it:
WEIGHT, LIFT, THRUST and DRAG.

These are all closely interrelated, i.e.:
The greater the weight - the greater the lift requirement.
The greater the lift - the greater the drag.
The greater the drag - the greater the thrust required, and so on ...

Air has properties which change with altitude. Knowledge of these variables, together with
their effect on an aeroplane, is a prerequisite for a full understanding of the principles of flight.
The structural and aerodynamic design of an aeroplane is a masterpiece of compromise. An
improvement in one area frequently leads to a loss of efficiency in another.
An aeroplane does not ‘grip’ the air as a car does the road. An aeroplane is often not pointing
in the same direction in which it is moving.

6

1Overview and Definitions Overview and Definitions 1

General Definitions

Mass

Unit - Kilogram (kg) - ‘The quantity of matter in a body.’ The mass of a body is a measure of
how difficult it is to start or stop. (a “body”, in this context, means a substance. Any substance:
a gas, a liquid or a solid.)

• The larger the mass, the greater the FORCE required to start or stop it in the same distance.

• Mass has a big influence on the time and/or distance required to change the direction of a
body.

Force

Unit - newton (N) - ‘A push or a pull’. That which causes or tends to cause a change in motion
of a body.

There are four forces acting on an aircraft in flight - pushing or pulling in different directions.

Weight

Unit - newton (N) - ‘The force due to gravity’. ( F = m × g )

where (m) is the mass of the object and (g) is the acceleration due to the gravity constant,
which has the value of 9.81 m/s2. ( A 1 kg mass ‘weighs’ 9.81 newtons )

If the mass of a B737 is 60 000 kg

and F = m × g

it is necessary to generate: [60 000 kg × 9.81 m/s2]

588 600 N of lift force.

Centre of Gravity (CG)

The point through which the weight of an aircraft acts.

• An aircraft in flight rotates around its CG.

• The CG of an aircraft must remain within certain forward and aft limits, for reasons of both
stability and control.

Work

Unit - Joule (J) - A force is said to do work on a body when it moves the body in the direction
in which the force is acting. The amount of work done on a body is the product of the force
applied to the body and the distance moved by that force in the direction in which it is acting.
If a force is exerted and no movement takes place, no work has been done.

• Work = Force × Distance (through which the force is applied)

• I f a force of 10 newtons moves a body 2 metres along its line of action, it does 20 newton
metres (Nm) of work. [10 N × 2 m = 20 Nm]

• A newton metre, the unit of work, is called a joule (J).

7

1 Overview and Definitions

1 Overview and Definitions Power

Unit - Watt (W) - Power is simply the rate of doing work (the time taken to do work).

• Power (W) = Force (N) × Distance (m)
Time (s)

• I f a force of 10 N moves a mass 2 metres in 5 seconds, then the power is 4 joules per second.
A joule per second (J/s) is called a watt (W), the unit of power. So the power used in this
example is 4 watts.

Energy

Unit - Joule (J) - Mass has energy if it has the ability to do work. The amount of energy a body

possesses is measured by the amount of work it can do. The unit of energy will, therefore, be

the same as those of work, joules.

Kinetic Energy

Unit - Joule (J) - ’The energy possessed by mass because of its motion’. ’A mass that is moving

can do work in coming to rest’.

KE = ½mV2 joules

The kinetic energy of a 1 kg mass of air moving at 52 m/s (100 knots) is 1352 joules; it possesses
1352 joules of kinetic energy. [ 0.5 × 1 × 52 × 52 = 1352 J ]

From the above example it can be seen that doubling the velocity will have a greater impact on
the kinetic energy than doubling the mass (velocity is squared).

Newton’s First Law of Motion

’A body will remain at rest or in uniform motion in a straight line unless acted on by an external
force’.

To move a stationary object or to make a moving object change its direction, a force must be
applied.

Inertia

‘The opposition which a body offers to a change in motion’. A property of all bodies, inertia is
a quality, but it is measured in terms of mass, which is a quantity.

• The larger the mass, the greater the force required for the same result.
• A large mass has a lot of inertia.
• Inertia refers to both stationary and moving masses.

Newton’s Second Law of Motion

’The acceleration of a body from a state of rest, or uniform motion in a straight line, is
proportional to the applied force and inversely proportional to the mass’.

Velocity

Unit - Metres per second (m/s). - ‘Rate of change of displacement’

8

1Overview and Definitions

Acceleration Overview and Definitions 1

Unit - Metres per second per second (m/s2) - ‘Rate of change of velocity’.

A force of 1 newton acting on a mass of 1 kg will produce an acceleration of 1 m/s2

Acceleration = Force
Mass

• For the same mass; the bigger the force, the greater the acceleration.
• For the same force; the larger the mass, the slower the acceleration.

Momentum

Unit - Mass × Velocity (kg-m/s) - ‘The quantity of motion possessed by a body’. The tendency
of a body to continue in motion after being placed in motion.

• A body of 10 kg mass moving at 2 m/s has 20 kg-m/s of momentum.
• At the same velocity, a large mass has more momentum than a small mass.

Newton’s Third Law

‘Every action has an equal and opposite reaction’

• If a force accelerates a mass in one direction, the body supplying the force will be subject to
the same force in the opposite direction.

9

1 Overview and Definitions 1 Overview and Definitions

Glossary

Aerofoil - A body so shaped as to produce aerodynamic reaction normal to the direction of its
motion through the air without excessive drag.

Aft - To the rear, back or tail of the aircraft.

Air brake - Any device primarily used to increase drag of an aircraft at will.

Ambient - Surrounding or pertaining to the immediate environment.

Amplitude - Largeness; abundance; width; range; extent of repetitive movement (from
extreme to extreme).

Attitude - The nose-up or nose-down orientation of an aircraft relative to the horizon.

Boundary Layer - The thin layer of air adjacent to a surface, in which the viscous forces are
dominant.

Buffeting - An irregular oscillation of any part of an aircraft produced and maintained directly
by an eddying flow.

Cantilever (wing) - A wing whose only attachment to the fuselage is by fittings at the wing root:
it has no external struts or bracing. The attachments are faired-in to preserve the streamline
shape

Control Lock (Gust lock) - A mechanical device designed to safeguard, by positive lock, the
control surfaces and flying control system against damage in high winds or gusts when the
aircraft is parked.

Control Reversal - At high speed: the displacement of a control surface producing a moment
on the aircraft in a reverse sense because of excessive structural distortion. At low speed: the
displacement of an aileron increasing the angle of attack of one wing to or beyond the critical
angle, causing a roll in the direction opposite to that required.

Convergent - Tend towards or meet in one point or value.

Critical Mach Number (MCRIT) - The free stream Mach number at which the peak velocity on the
surface of a body first becomes equal to the local speed of sound.

Damping - To slow down the rate; to diminish the amplitude of vibrations or cycles.

Geometric Dihedral - The angle between the horizontal datum of an aeroplane and the plane
of a wing or horizontal stabilizer semi-span.

Divergent - Inclined or turned apart. Divergence - A disturbance which increases continually
with time.

Eddy - An element of air having intense vorticity.

Effective Angle of Attack (αe) - The angle between the chord line and the mean direction of a
non-uniform disturbed airstream.

10

1Overview and Definitions

Equilibrium - A condition that exists when the sum of all moments acting on a body is zero Overview and Definitions 1
AND the sum of all forces acting on a body is zero.

Fairing - A secondary structure added to any part to reduce its drag.

Feel - The sensations of force and displacement experienced by the pilot from the aerodynamic
forces on the control surfaces.

Fence - A projection from the surface of the wing and extending chordwise to modify the wing
surface pressure distribution.

Fillet - A fairing at the junction of two surfaces to improve the airflow.

Flight Path - The path of the Centre of Gravity (CG) of an aircraft.

Fluid - A substance, either gaseous or liquid, that will conform to the shape of the container
that holds it.

Free Stream Velocity - The velocity of the undisturbed air relative to the aircraft.

Gradient (Pressure) - Rate of change in pressure with distance.

Gust - A rapid variation, with time or distance, in the speed or direction of air.

Gust Lock - See control lock.

Instability - The quality whereby any disturbance from steady motion tends to increase.

Laminar Flow - Flow in which there is no mixing between adjacent layers.

Load Factor - The ratio of the weight of an aircraft to the load imposed by lift. The correct
symbol for load factor is (n), but it is colloquially known as (g).

Load Factor = Lift
Weight

Mach Number (M) - The ratio of the True Airspeed to the speed of sound under prevailing
atmospheric conditions.

M = TAS
Local Speed of Sound (a)

Magnitude - Largeness; size; importance.

Moment (N-m) - The moment of a force about a point is the product of the force and the
distance through which it acts. The distance in the moment is merely a leverage and no
movement is involved, so moments cannot be measured in joules.

Nacelle - A streamlined structure on a wing for housing engines (usually).

Normal - Perpendicular; at 90°.

Oscillation - Swinging to and fro like a pendulum; a vibration; variation between certain
limits; fluctuation.

Parallel - Lines which run in the same direction and which will never meet or cross.

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1 Overview and Definitions 1 Overview and Definitions

Pitot Tube - A tube, with an open end facing up-stream, wherein at speeds less than about four
tenths the speed of sound the pressure is equal to the total pressure. For practical purposes,
total pressure may be regarded as equal to pitot pressure at this stage.

Pod - A nacelle supported externally from a fuselage or wing.

Propagate - To pass on; to transmit; to spread from one to another.

Relative Airflow, (Relative Wind), (Free Stream Flow) - The direction of airflow produced
by the aircraft moving through the air. The relative airflow flows in a direction parallel and
opposite to the direction of flight. Therefore, the actual flight path of the aircraft determines
the direction of the relative airflow. Also, air in a region where pressure, temperature and
relative velocity are unaffected by the passage of the aircraft through it.

Scale - If a 1/10th scale model is considered, all the linear dimensions are 1/10th of the real
aircraft, but the areas are 1/100th; and if the model is constructed of the same materials, the
mass is 1/1000th of the real aircraft. So the model is to scale in some respects, but not others.

Schematic - A diagrammatic outline or synopsis; an image of the thing; representing something
by a diagram.

Separation - Detachment of the airflow from a surface with which it has been in contact.

Shock Wave - A narrow region, crossing the streamlines, through which there occur abrupt
increases in pressure, density, and temperature, and an abrupt decrease in velocity. The
normal component of velocity relative to the shock wave is supersonic upstream and subsonic
downstream.

Side-slip - Motion of an aircraft, relative to the relative airflow, which has a component of
velocity along the lateral axis.

Slat - An auxiliary, cambered aerofoil positioned forward of the main aerofoil so as to form a
slot.

Spar - A principal spanwise structural member of a wing, tailplane, fin or control surface.

Speed - Metres per second (m/s) is used in most formulae, but nautical miles per hour or knots
(kt) are commonly used to measure the speed of an aircraft. There are 6080 ft in 1 nautical
mile and 3.28 ft in 1 metre.

Speed of Sound (a) - Sound is pressure waves which propagate spherically through the
atmosphere from their source. The speed of propagation varies ONLY with the temperature of
the air. The lower the temperature, the lower the speed of propagation. On a ’standard’ day
at sea level the speed of sound is approximately 340 m/s (660 kt TAS).

Stability - The quality whereby any disturbance of steady motion tends to decrease.

Stagnation Point - A point where streamlines are divided by a body and where the fluid speed
is zero, relative to the surface.

Static Vent - A small aperture in a plate fixed to form part of the fuselage and located
appropriately for measuring the ambient static pressure.

Throat - A section of minimum area in a duct.

12

1Overview and Definitions

True Airspeed (TAS) or (V) - The speed at which the aircraft is travelling through the air. Overview and Definitions 1

Turbulent Flow - Flow in which irregular fluctuations with time are superimposed on a mean
flow.

Velocity - The same as speed, but with direction specified as well.

Viscosity - The resistance of fluid particles to flow over each other. All fluids have the property
of viscosity. A fluid with high viscosity would not flow very easily. The viscosity of air is low
in comparison to something like syrup, but the viscosity that air does have is a very important
consideration when studying aerodynamics.

Vortex - A region of fluid in circulatory motion, having a core of intense vorticity, the strength
of the vortex being given by its circulation.

Vortex Generator - A device, often a small vane attached to a surface, to produce one or
more discrete vortices which trail downstream adjacent to the surface, promote mixing in
the boundary layer and delay boundary layer separation. (Increases the kinetic energy of the
boundary layer).

Vorticity - Generally, rotational motion in a fluid, defined, at any point in the fluid, as twice the
mean angular velocity of a small element of fluid surrounding the point.

Wake - The region of air behind an aircraft in which the total pressure has been changed by the
presence of the aircraft.

Wash-out - Decrease in angle of incidence towards the tip of a wing or other aerofoil.

Wing Loading - Ratio of aircraft weight to wing area.

Wing Loading = Aircraft Weight
Wing Area

Zoom - Using kinetic energy to gain height.

13

1 Overview and Definitions 1 Overview and Definitions

List of Symbols

The following symbols are used throughout these notes. However, no universal defining
standard for their use exists. Other books on the subject may use some of these symbols with
different definitions. Every effort has been made to employ symbols that are widely accepted
and that conform to the Learning Objectives.

a speed of sound
AC aerodynamic centre
AR aspect ratio
b span
C Centigrade
c chord length
CD drag coefficient
CG centre of gravity
CP centre of pressure
CL lift coefficient
CM pitching moment coefficient
D drag
Di induced drag
F force
g acceleration due to gravity, also used for load factor
K Kelvin
L lift
L/D lift to drag ratio
M Mach number
m mass
n load factor
p pressure
Q or q dynamic pressure
S area; wing area
T temperature
t/c thickness-chord ratio
V free stream speed (TAS)
VS stall speed
W weight

Greek Symbols

α (alpha) angle of attack
β (beta) sideslip angle
γ (gamma) angle of climb or descent
Δ (delta) increment in
μ (mu) Mach angle
ρ (rho) density
σ (sigma) relative density
φ (phi) angle of bank

14

1Overview and Definitions Overview and Definitions 1

Others

∝ proportional to
••= is approximately equal to
Note: The Greek symbol γ (gamma) has been used in these notes to denote angle of climb and
descent. The Learning Objectives use θ (theta). Evidence exists that a question in the exam uses
γ (gamma) for angle of climb and descent. The notes have been amended to use γ, but consider
either γ or θ to indicate angle of climb and descent.

15

1 Questions

1 Questions Self-assessment Questions

Aircraft (1)
Mass: 2000 kilograms (kg)
Engine thrust: 4000 newtons (N)
V1 speed: 65 knots (kt)
Take-off run to reach V1: 750 metres (m)
Time taken to reach V1: 30 seconds (s)

Aircraft (2)
Mass: 2000 kilograms (kg)
Engine thrust: 8000 newtons (N)
V1 speed: 130 knots (kt)
Take-off run to reach V1: 1500 metres (m)
Time taken to reach V1: 40 seconds (s)

where 1 nautical mile = 6080 ft and 1 metre = 3.28 ft

At V1 both aircraft experience an engine failure and take-off is abandoned.

a. How much wpwmmptioomoooowwrrmmekkeeseerrwwgnnwwraatteuussaaammssddteoouuddrssnneeooieesddeetttssoohttooaaeaaiirrggmiiccrreeccrroaattrraamffaattffiitterr((ccn12((rr12))taau))ppffmttggooee((ss21ottsstt))eefiissnnttassooggiraaVVcttttroo11aVV??fVV11t??11(??2)?
b. How much
c. How much
d. How much
e. How much
f. How much
g. How many
h. How much kinetic energy does kaaiiinrrccerrtaaicfftte((n21e))rppgooyssosseefssassiraacttraVVf11t??(2)?
i. How much kinetic energy does
j. How many times greater is the
k. State the mass and velocity relationship of both aircraft and compare to their
momentum and kinetic energy.
l. Which has the greater effect on kinetic energy, mass or velocity?
m. What must be done with the kinetic energy so the aircraft can be brought to a
stop?

16

1Questions Questions 1

1. An aircraft’s mass is a result of:
a. its weight.
b. how big it is.
c. how much matter it contains.
d. its volume.

2. The unit of mass is the:
a. joule.
b. watt.
c. newton.
d. kilogram.

3. The definition of a force is:
a. that which causes a reaction to take place.
b. thrust and drag only.
c. a push or a pull.
d. the result of an applied input.

4. The unit of force is the:
a. mass-kilogram.
b. newton-metre.
c. joule.
d. newton.

5. The unit of weight is the:
a. kilogram.
b. newton.
c. watt.
d. kilowatt.

6. Weight is the result of:
a. the force on mass due to gravity.
b. the action of a falling mass.
c. how much matter the object contains.
d. the rate of mass per unit area.

7. About which point does an aircraft rotate?
a. The wings.
b. The main undercarriage.
c. The centre of gravity.
d. The rudder.

8. If a force is applied to a mass and the mass does not move:
a. work is done even though there is no movement of the mass.
b. work is done only if the mass moves a long way.
c. power is exerted, but no work is done.
d. no work is done.

17

1 Questions 1 Questions

9. The unit of work is called the:
a. pascal.
b. joule.
c. watt.
d. kilogram.

10. The unit of power is called the:
a. joule.
b. newton-metre.
c. watt.
d. metre per second.

11. If a force of 20 newtons moves a mass 5 metres:
1 - the work done is 100 Nm
2 - the work done is 100 joules
3 - the work done is 4 joules
4 - the work done is 0.25 joules
The correct statements are:

a. 1 only.
b. 1 and 3.
c. 1 and 2.
d. 2 only.
12. If a force of 50 newtons is applied to a 10 kg mass and the mass moves 10 metres
and a force of 50 newtons is applied to a 100 kg mass which moves 10 metres:
a. the work done is the same in both cases.
b. less work is done to the 10 kg mass.
c. more work is done to the 10 kg mass.
d. more work is done to the 100 kg mass.
13. The definition of power is:
a. the rate of force applied.
b. the rate of movement per second.
c. the rate of doing work.
d. the rate of applied force.
14. If a force of 500 newtons moves a mass 1000 metres in 2 mins, the power used is:
a. 4167 watts.
b. 250 kilowatts.
c. 1 megawatt.
d. 4 watts.
15. Kinetic energy is:
a. the energy a mass possesses due to its position in space.
b. the energy a mass possesses when a force has been applied.
c. the energy a mass possesses due to the force of gravity.
d. the energy a mass possesses because of its motion.

18

1Questions Questions 1

16. The unit of kinetic energy is the:
a. joule.
b. metre per second.
c. watt.
d. newton-metre per second.

17. When considering kinetic energy:
1 - a moving mass can apply a force by being brought to rest.
2 - kinetic energy is the energy possessed by a body because of its motion.
3 - if a body’s kinetic energy is increased, a force must have been applied.
4 - kinetic energy = ½ m V2 joules.
The combination of correct statements is:

a. 1 and 2.
b. 1, 2, 3 and 4.
c. 4 only.
d. 2 and 4.
18. The property of inertia is said to be:
a. the energy possessed by a body because of its motion.
b. the opposition which a body offers to a change in motion.
c. that every action has an equal and opposite reaction.
d. the quantity of motion possessed by a body.
19. Considering Newton’s first law of motion:
1 - a body is said to have energy if it has the ability to do work.
2 - t he amount of energy a body possesses is measured by the amount of work it

can do.
3 - a body will tend to remain at rest, or in uniform motion in a straight line, unless

acted upon by an external force.
4 - t o move a stationary object or to make a moving object change its direction, a

force must be applied.
The combination with the correct statements is:

a. 3 and 4.
b. 3 only.
c. 1 and 2.
d. 1, 2, 3 and 4.

19

1 Questions 1 Questions

20. Considering Newton’s second law of motion:
1 - every action has an equal and opposite reaction.
2 - if the same force is applied, the larger the mass the slower the acceleration.
3 - if two forces are applied to the same mass, the bigger the force the greater the

acceleration.
4 - the acceleration of a body from a state of rest, or uniform motion in a straight

line, is proportional to the applied force and inversely proportional to the mass.
The combination of true statements is:

a. 1 only.
b. 1, 2, 3 and 4.
c. 2, 3, and 4.
d. 3 and 4.
21. Newton’s third law of motion states:
a. the energy possessed by a mass is inversely proportional to its velocity.
b. every force has an equal and opposite inertia.
c. for every force there is an action.
d. every action has an equal and opposite reaction.
22. The definition of velocity is the:
a. rate of change of acceleration.
b. rate of change of displacement.
c. the quantity of motion possessed by a body.
d. the acceleration of a body in direct proportion to its mass.
23. When considering acceleration:
1 - acceleration is the rate of change of velocity.
2 - the units of acceleration are metres per second.
3 - the units of acceleration are kilogram-metres per second.
4 - the units of acceleration are seconds per metre per metre.
The combination of correct statements is:
a. 4 only.
b. 1 and 4.
c. 1 only.
d. 1 and 2.
24. The definition of momentum is:
a. the quantity of mass possessed by a body.
b. the quantity of inertia possessed by a body.
c. the quantity of motion possessed by a body.
d. the opposition which a body offers to a change in velocity.

20

1Questions Questions 1

25. A force of 24 newtons moves a 10 kg mass 60 metres in 1 minute. The power used
is:

1 - 24 watts.
2 - 240 watts.
3 - force times distance moved in one second.
4 - force times the distance the mass is moved in one second.
Which of the preceding statements are correct:

a. 1 and 3.
b. 1, 3 and 4.
c. 2 and 4.
d. 4 only.
26. When considering momentum:
1 - momentum is the quantity of motion possessed by a body.
2 - m omentum is the tendency of a body to continue in motion after being placed

in motion.
3 - a mass of 2000 kg moving at 55 m/s has 110 000 kg-m/s of momentum.
4 - a large mass moving at 50 m/s will have less momentum than a small mass

moving at 50 m/s.
The correct combination of statements is:

a. 1 and 3.
b. 1, 2, 3 and 4.
c. 1, 2 and 3.
d. 2, 3 and 4.

21

1 Answers 1 Answers

Answers

Aircraft number (1) V1 speed of 65 knots = 33.5 m/s
Aircraft number (2) V1 speed of 130 knots = 67 m/s

a. 3 000 000 joules
b. 100 000 watts
c. 12 000 000 joules
d. 300 000 watts
e 67 000 kg-m/s
f. 134 000 kg-m/s
g. twice
h. 1 122 250 joules
i. 4 489 000 joules
j. four times greater
k. same mass, speed doubled, momentum doubled, but kinetic energy four

times greater.
l. velocity has a greater effect on kinetic energy than mass.
m. it must be dissipated by the braking systems.
1 2 3 4 5 6 7 8 9 10 11 12
cdcdba cdbc c a
13 14 15 16 17 18 19 20 21 22 23 24
c adabba cdbc c
25 26
bc

22

2Chapter

The Atmosphere

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
The Physical Properties of Air . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Static Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Air Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
International Standard Atmosphere (ISA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Dynamic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Key Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Measuring Dynamic Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Relationships between Airspeeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Airspeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
Errors and Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
V Speeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

23

2 The Atmosphere 2 The Atmosphere

24

2The Atmosphere The Atmosphere 2

Introduction

The atmosphere is the medium in which an aircraft operates. It is the properties of the
atmosphere, changed by the shape of the wing, that generate the required lift force.

The most important property is air density (the “thickness” of air).

KEY FACT: If air density decreases, the mass of air flowing over the aircraft in a given time will
decrease. Not usually considered during the study of Principles of Flight, keeping the idea of
mass flow (kg/s) in the ‘back of your mind’ can aid general understanding.

A given mass flow will generate the required lift force, but a decrease in air density will reduce
the mass flow.

To maintain the required lift force if density decreases, the speed of the aircraft through the air
must be increased. The increased speed of airflow over the wing will maintain the mass flow
and lift force at its required value.

The Physical Properties of Air

Air has substance! Air has mass; not very much if compared to other matter, but nevertheless
a significant amount. A mass of moving air has considerable kinetic energy; for example,
when moving at 100 knots the kinetic energy of air can inflict severe damage to man-made
structures.

Air is a compressible fluid and is able to flow or change its shape when subjected to even
minute pressure differences. (Air will flow in the direction of the lower pressure). The viscosity
of air is so low that very small forces are able to move the molecules in relation to each other.

When considering the portion of atmosphere in which most aircraft operate (up to 40 000 ft),
with increasing altitude the characteristics of air undergo a gradual transition from those at
sea level. Since air is compressible, the lower layers contain much the greater part of the whole
mass of the atmosphere. Pressure falls steadily with increasing altitude, but temperature falls
steadily only to about 36 000 ft, above which it then remains constant through the stratosphere.

Static Pressure

The unit for static pressure is N/m2, the symbol is lower case ‘p’.

• Static pressure is the result of the weight of the atmosphere pressing down on the air
beneath.

• S tatic pressure will exert the same force per square metre on all surfaces of an aeroplane.
The lower the altitude, the greater the force per square metre.

• It is called static pressure because of the air’s stationary or static presence.

• An aircraft always has static pressure acting upon it.

Newtons per square metre is the SI unit for pressure. 1 N/m2 is called a pascal and is quite a
small unit. In aviation the hectopascal (hPa) is used. (‘hecto’ means 100 and 1 hectopascal is
the same as 1 millibar).

25

2 The Atmosphere

2 The Atmosphere Static pressure at a particular altitude will vary from day to day, and is about 1000 hPa at sea
level. In those countries that measure static pressure in inches of mercury (inHg), sea level
static pressure is about 30 inHg.

Temperature

The unit for temperature is °C, or K. It is degrees Celsius (or centigrade) when measured relative
to the freezing point of water, or Kelvin when measured relative to absolute zero. (0°C is
equivalent to 273 K).

Temperature decreases with increasing altitude up to about 36 000 ft and then remains
constant.

Air Density

The unit for density is kg/m3 and the symbol is the Greek letter ρ [rho].

• Density is ‘mass per unit volume’ (The ‘number’ of air particles in a given space).
• Density varies with static pressure, temperature and humidity.

• Density decreases if static pressure decreases.
• Density decreases if temperature increases.
• Density decreases if humidity increases.

Air Density is proportional to pressure and inversely proportional to temperature. This is shown
in the ideal gas law formula below.

P = constant, more usefully it can be said that ρ ∝ P
Tρ T

where p = pressure, T = temperature, and ρ = density

Density decreases with increasing altitude because of decreasing static pressure. However,
with increasing altitude temperature also decreases, which would tend to increase density, but
the effect of decreasing static pressure is dominant.

International Standard Atmosphere (ISA)

The values of temperature, pressure and density are never constant in any given layer of the
atmosphere. To enable accurate comparison of aircraft performance and the calibration of
pressure instruments, a ‘standard’ atmosphere has been adopted. The standard atmosphere
represents the mean or average properties of the atmosphere.

Europe uses the standard atmosphere defined by the International Civil Aviation Organization
(ICAO).

The ICAO standard atmosphere assumes the following mean sea level values:

Temperature 15°C
Pressure 1013.25 hPa
Density 1.225 kg/m3

26

2The Atmosphere

The temperature lapse rate is assumed to be uniform at a rate of 2°C per 1000 ft (1.98°C) from The Atmosphere 2
mean sea level up to a height of 36 090 ft (11 000 m) above which the lapse rate becomes zero
and the temperature remains constant at -56.5°C.

ICAO Standard Atmosphere

Altitude Temperature Pressure (hPa) Density (kg/m3) Relative Density
(ft) (°C) (p) (ρ) (σ)
- 56.5 116.0 0.15
50 000 - 56.5 147.5 0.186 0.19
45 000 - 56.5 0.237 0.25
40 000 - 54.3 187.6 0.302 0.31
35 000 - 44.4 238.4 0.386 0.37
30 000 - 34.5 300.9 0.458 0.45
25 000 - 24.6 376.0 0.549 0.53
20 000 - 14.7 465.6 0.653 0.63
15 000 - 4.8 571.8 0.771 0.74
10 000 5.1 696.8 0.905 0.86
5000 15 843.1 1.056 1.0
Sea Level 1013.25 1.225

NOTE: High Density Altitude means that the conditions that actually exist at the airport of take-
off or landing represent those of a higher altitude in the International Standard Atmosphere i.e.
less air density.

Dynamic Pressure

The unit for dynamic pressure is N/m2 and the symbol is lower case ‘q’ or upper case ‘Q’.

• Because air has mass, air in motion must possess kinetic energy, and will exert a force per
square metre on any object in its path. (KE = ½ m V2)

• It is called DYNAMIC pressure because the air is moving in relation to the object being
considered, in this case an aircraft.

• D ynamic pressure is proportional to the density of the air and the square of the speed of
the air flowing over the aircraft.

An aircraft immersed in moving airflow will therefore experience both static AND dynamic
pressure. (Remember, static pressure is always present).

27

2 The Atmosphere 2 The Atmosphere

The kinetic energy of one cubic metre of air moving at a stated speed is given by the formula:
Kinetic Energy = ½ ρ V2 joules

where ρ is the local air density in kg/m3 and V is the speed in m/s
If this cubic metre of moving air is completely trapped and brought to rest by means of an
open-ended tube the total energy will remain constant, but by being brought completely to
rest the kinetic energy will become pressure energy which, for all practical purposes, is equal
to:

Dynamic Pressure = ½ ρ V2 N/m2
Consider air flowing at 52 m/s (100 kt) with a density of 1.225 kg/m3
(100 kt = 100 NM/h = 100 × 6080 ft/h = 608 000 ÷ 3.28 = 185 366 ÷ 60 ÷ 60 m/s = 52 m/s)

Dynamic pressure = 0.5 × 1.225 × 52 × 52 = 1656 N/m2 (16.56 hPa)
If speed is doubled, dynamic pressure will be four times greater
0.5 × 1.225 × 104 × 104 = 6625 N/m2 (66.25 hPa)

If the cross-sectional area of the tube is 1 m2 a force of ½ ρ V2 newtons will be generated.
(Force = Pressure × Area)
Dynamic pressure ( ½ ρ V2 ) is common to ALL aerodynamic forces and determines the air
loads imposed on an aeroplane moving through the air.
The symbol for dynamic pressure ( ½ ρ V2 ) is q or Q

Q = ½ ρ V2

28

2The Atmosphere The Atmosphere 2

Key Facts

A pilot needs to know how much dynamic pressure is available, but dynamic pressure cannot
be measured on its own because static pressure will always be present. The sum of static and
dynamic pressure, in this context, is known as ‘Total’ pressure.
(Dynamic + Static pressure can also be referred to as Stagnation or Pitot pressure).

Total Pressure = Static Pressure + Dynamic Pressure
This can be re-arranged to show that:

Total Pressure - Static Pressure = Dynamic Pressure
The significance of dynamic pressure to the understanding of Principles of Flight cannot be
overemphasized.
Because dynamic pressure is dependent upon air density and the speed of the aircraft through
the air, it is necessary for students to fully appreciate the factors which affect air density.
• Temperature - increasing temperature decreases air density. Changes in air density due to

air temperature are significant during all phases of flight.
• Static pressure - decreasing static pressure decreases air density. Changes in air density due

to static pressure are significant during all phases of flight.
• Humidity - increasing humidity decreases air density. (The reason increasing humidity

decreases air density is that the density of water vapour is about 5/8 that of dry air).
Humidity is most significant during take-off and landing.
Increasing altitude will decrease air density because the effect of decreasing static pressure is
more dominant than decreasing temperature.

29

2 The Atmosphere

2 The Atmosphere Measuring Dynamic Pressure

All aerodynamic forces acting on an aircraft are determined by dynamic pressure, so it is
essential to have some means of measuring dynamic pressure and presenting that information
to the pilot.

A sealed tube, open at the forward end, is located where it will collect air when the aircraft is
moving. The pressure in the tube (pitot tube) is Dynamic + Static and, in this context, is called
“Pitot” pressure (because the air is inside the pitot tube).

Some way of ‘removing’ the static pressure from the pitot pressure must be found. A hole
(vent) in a surface parallel to the airflow will sense static pressure. Referring to the diagram
below, if the pressure from the pitot tube is fed to one side of a diaphragm mounted in a
sealed case, and static pressure is fed to the other side, the two static pressures will cancel each
other and the diaphragm movement will be influenced only by changes in dynamic pressure.

Movement of the diaphragm moves a pointer over a scale so that changes in dynamic pressure
can be observed by the flight crew. But the instrument is calibrated at ISA sea level density,
so the instrument will only give a ‘true’ indication of the speed of the aircraft through the air
when the air density is 1.225 kg/m3.

This is not a problem because the pilot needs an indication of dynamic pressure, and this is
what the instrument provides. The instrument is made in such a way that it indicates the
square root of the dynamic pressure in nautical miles per hour (knots) or statute miles per hour
(mph). So, if this “Indicated Airspeed” is doubled, the speed of the aircraft through the air
will also be doubled.

A irf low PITOT PRESSURE The Airspeed Indicator
PITOT TUBE (Static + Dynamic) is a pressure gauge

Needle indicates
changes in
DYNAMIC PRESSURE

Airflow STAT IC
STATIC VENT PRESSURE

Figure 2.1 Schematic of the airspeed indicator (ASI)

30

2The Atmosphere

Relationships between Airspeeds

Indicated Airspeed: (IAS). The speed registered on the Airspeed Indicator. The Atmosphere 2

Calibrated Airspeed: (CAS). An accurate measure of dynamic pressure when the aircraft is
flying slowly. The position of the pitot tube(s) and static vent(s), together with the aircraft’s
configuration (flaps, landing gear etc.) and attitude to the airflow (angle of attack and sideslip)
will affect the pressures sensed, particularly the pressures sensed at the static vent(s).

Under the influence of the above conditions a false dynamic pressure (IAS) will be displayed.
When IAS is corrected for this ‘position’ or ‘pressure’ error, as it is called, the resultant is
Calibrated Airspeed. (The airspeed corrections to be applied may be displayed on a placard on
the flight-deck, or in the Flight Manual, and will include any instrument error).

Equivalent Airspeed: (EAS). An accurate measure of dynamic pressure when the aircraft is
flying fast. Air entering the pitot tube(s) is compressed, which gives a false dynamic pressure
(IAS) reading, but only becomes significant at higher speeds.

At a given air density, the amount of compression depends on the speed of the aircraft through
the air. When the IAS is corrected for ‘position’ AND ‘compressibility’ error, the resultant is
Equivalent Airspeed.

True Airspeed: (TAS) or (V). The speed of the aircraft through the air. THE ONLY SPEED
THERE IS - All the other, so called, speeds are pressures.

TAS = E√ AбS Where, б is Relative Density

The Airspeed Indicator is calibrated for ‘standard’ sea level density, so it will only read TAS if the

density of the air through which the aircraft is flying is 1.225 kg/m3. Thus at 40 000 ft where the

‘standard’ density is one quarter of the sea-level value, to maintain the same EAS the aircraft

will have to move through the air twice as fast!

The Speed of Sound: (a) Sound is ‘weak’ pressure waves which propagate spherically
through the atmosphere from their source. The speed at which pressure waves propagate
is proportional to the square root of the absolute temperature of the air. The lower the
temperature, the lower the speed of propagation. On a ‘standard’ day at sea level the speed
of sound is approximately 340 m/s (660 kt TAS).

At higher aircraft True Airspeeds (TAS) and/or higher altitudes, it is essential to know the speed
of the aircraft in relation to the local speed of sound. This speed relationship is known as the
Mach Number (M).

M = T(Aa)S Where (a) is the Local Speed of Sound

If the True Airspeed of the aircraft is four tenths the speed at which pressure waves propagate
through the air mass surrounding the aircraft, the Mach meter will register M 0.4

Critical Mach Number: (MCRIT) The critical Mach number is the Mach number of the aircraft
when the speed of the airflow over some part of the aircraft (usually the point of maximum
thickness on the aerofoil) first reaches the speed of sound.

31

2 The Atmosphere 2 The Atmosphere

Airspeed

This information is to reinforce that contained in the preceding paragraphs.

The airspeed indicator is really a pressure gauge, the ‘needle’ of which responds to changes in
dynamic pressure (½ ρ V2 ).

The Airspeed Indicator
is a Pressure Gauge

Calibration of the airspeed indicator is based on standard sea level density (1.225 kg/m3). The
“airspeed” recorded will be different from the actual speed of the aircraft through the air
unless operating under standard sea level conditions (unlikely). The actual speed of the aircraft
relative to the free stream is called true airspeed (TAS), and denoted by (V). The ‘speed’
recorded by the airspeed indicator calibrated as above, if there are no other errors, is called
equivalent airspeed (EAS).

It may seem to be a drawback that the instrument records equivalent rather than true
airspeed, but the true airspeed may always be determined from it. Also, many of the handling
characteristics of an aircraft depend mainly on the dynamic pressure, i.e. on the equivalent
airspeed, so it is often more useful to have a direct reading of EAS than TAS.

Errors and Corrections

An airspeed indicator is, however, also subject to errors other than that due to the difference
between the density of the air through which it is flying and standard sea level density.

• Instrument Error: This error may arise from the imperfections in the design and manufacture
of the instrument, and varies from one instrument to another. Nowadays this type of
error is usually very small and for all practical purposes can be disregarded. Where any
instrument error does exist, it is incorporated in the calibrated airspeed correction chart for
the particular aeroplane.

• P osition Error (Pressure Error): This error is of two kinds, one relating to the static pressure
measurement, the other to the pitot (total) pressure measurement. The pitot tube(s) and
static port(s) may be mounted in a position on the aircraft where the flow is affected by
the presence of the aircraft, changes in configuration (flaps and maybe gear) and proximity
to the ground (ground effect). If so, the static pressure recorded will be the local and
not the free stream value. The pitot pressure may be under-recorded because of incorrect
alignment - the tube(s) may be inclined to the airstream instead of facing directly into it
(changes in angle of attack, particularly at low speeds). The magnitude of the consequent
errors will generally depend on the angle of attack and, hence, the speed of the aircraft.

• C ompressibility Error: At high speeds, the dynamic pressure is not simply ½ ρ V2, but exceeds
it by a factor determined by Mach number. Thus the airspeed indicator will over-read.

Because of the errors listed, the ‘speed’ recorded on the airspeed indicator is generally not
the equivalent airspeed. It is called instead the indicated airspeed. Corrections to rectify
the instrument and position errors are determined experimentally. In flight, using special
instruments, measurements are taken over the whole range of speeds and configurations,
from which a calibration curve is obtained which gives the corrections appropriate to each
indicated airspeed. The compressibility error correction may be obtained by calculation.

32

2The Atmosphere The Atmosphere 2

The indicated airspeed, after correction for instrument, position (pressure) and compressibility
errors, gives the equivalent airspeed ½ ρ V2.

V Speeds

These include: VS , V1 , VR , V2 , VMD , VMC , VYSE and many others - these are all Calibrated
Airspeeds because they relate to aircraft operations at low speed. However, the appropriate
corrections are made and these speeds are supplied to the pilot in the Flight Manual as IAS.
VMO - The maximum operating IAS is, however, an EAS because it is a high speed, but again it is
supplied to the pilot in the Flight Manual as an IAS.

33

2 The Atmosphere 2 The Atmosphere

Summary

Dynamic pressure (Q) is affected by changes in air density.
Q = ½ ρ V2

Air density decreases if atmospheric pressure decreases.
Air density decreases if air temperature increases.
Air density decreases if humidity increases.
With the aircraft on the ground:
Taking off from an airfield with low atmospheric pressure and/or high air temperature
and/or high humidity will require a higher TAS to achieve the same dynamic pressure (IAS).
For the purpose of general understanding:
A constant IAS will give constant dynamic pressure.
Increasing altitude decreases air density because of decreasing static pressure.
With the aircraft airborne:
As altitude increases, a higher TAS is required to maintain a constant dynamic pressure.
Maintaining a constant IAS will compensate for changes in air density.
There is only one speed, the speed of the aircraft through the air, the TAS. All the other, so
called, speeds are pressures.
The Airspeed Indicator is a pressure gauge.
Aircraft ‘V’ speeds are CAS, except VMO which is an EAS, but all are presented to the pilot in the
Flight Manual as IAS.

34

2Questions Questions 2

Questions

1. When considering air:
1 - air has mass.
2 - air is not compressible.
3 - air is able to flow or change its shape when subject to even small pressures.
4 - the viscosity of air is very high.
5 - moving air has kinetic energy.
The correct combination of all true statements is:

a. 1, 2, 3 and 5.
b. 2, 3 and 4.
c. 1 and 4.
d. 1, 3, and 5.
2. Why do the lower layers contain the greater proportion of the whole mass of the
atmosphere?
a. Because air is very viscous.
b. Because air is compressible.
c. Because of greater levels of humidity at low altitude.
d. Because air has very little mass.
3. With increasing altitude, up to about 40 000 ft, the characteristics of air change:
1 - temperature decreases continuously with altitude.
2 - pressure falls steadily to an altitude of about 36 000 ft, where it then remains

constant.
3 - density decreases steadily with increasing altitude.
4 - pressure falls steadily with increasing altitude.
The combination of true statements is:

a. 3 and 4.
b. 1, 2 and 3.
c. 2 and 4.
d. 1 and 4.
4. When considering static pressure:
1 - in aviation, static pressure can be measured in hectopascals.
2 - the SI unit for static pressure is N/m2.
3 - static pressure is the product of the mass of air pressing down on the air

beneath.
4 - referred to as static pressure because of the air’s stationary or static presence.
5 - the lower the altitude, the greater the static pressure.
The correct statements are:

a. 2, 4 and 5.
b. 1, 2, 3, 4 and 5.
c. 1, 3 and 5.
d. 1 and 5.

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2 Questions 2 Questions

5. When considering air density:
1 - density is measured in millibars.
2 - density increases with increasing altitude.
3 - if temperature increases, the density will increase.
4 - as altitude increases, density will decrease.
5 - temperature decreases with increasing altitude, and this will cause air density to

increase
The combination of correct statements is:

a. 4 only.
b. 4 and 5.
c. 5 only.
d. 2, 3 and 5.
6. Air density is:
a. mass per unit volume.
b. proportional to temperature and inversely proportional to pressure.
c. independent of both temperature and pressure.
d. dependent only on decreasing pressure with increasing altitude.
7. When considering the ICAO International Standard Atmosphere and comparing it
with the actual atmosphere, which of the following statements is correct?
1 - T emperature, pressure and density are constantly changing in any given layer of

the actual atmosphere.
2 - A requirement exists for a hypothetical ’standard’ atmosphere.
3 - The values given in the International Standard Atmosphere exist at the same

altitudes in the actual atmosphere.
4- The International Standard Atmosphere was designed for the calibration of

pressure instruments and the comparison of aircraft performance calculations.
a. 1, 2 and 3.
b. 2, 3 and 4.
c. 1, 2, 3 and 4.
d. 1, 2 and 4.
8. When considering the ICAO International Standard Atmosphere, which of the
following statements is correct?
1 - T he temperature lapse rate is assumed to be uniform at 2°C per 1000 ft (1.98°C)

up to a height of 11 000 ft.
2 - Sea level temperature is assumed to be 15°C.
3 - Sea level static pressure is assumed to be 1.225 kg/m3.
4 - Sea level density is assumed to be 1013.25 hPa.

a. 1, 2, 3 and 4.
b. No statements are correct.
c. 1, 3 and 4.
d. 2 only.

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2Questions Questions 2

9. A moving mass of air possesses kinetic energy. An object placed in the path of
such a moving mass of air will be subject to which of the following?
a. Dynamic pressure.
b. Static pressure.
c. Static pressure and dynamic pressure.
d. Dynamic pressure minus static pressure.

10. Dynamic pressure is:
a. the total pressure at a point where a moving airflow is brought completely to
rest.
b. the amount by which the pressure rises at a point where a moving airflow is
brought completely to rest.
c. the pressure due to the mass of air pressing down on the air beneath.
d. the pressure change caused by heating when a moving airflow is brought
completely to rest.

11. Dynamic pressure is equal to:
a. density times speed squared.
b. half the density times the indicated airspeed squared.
c. half the true airspeed times the density squared.
d. half the density times the true airspeed squared.

12. A tube facing into an airflow will experience a pressure in the tube equal to:
a. static pressure.
b. dynamic pressure.
c. static pressure plus dynamic pressure.
d. the difference between total pressure and static pressure.

13. A static pressure vent must be positioned:
a. on a part of the aircraft structure where the airflow is undisturbed, in a
surface at right angles to the airflow direction.
b. on a part of the structure where the airflow is undisturbed, in a surface
parallel to the airflow direction.
c. at the stagnation point.
d. at the point on the surface where the airflow reaches the highest speed.

14. The inputs to an Airspeed Indicator are from:
a. a static source.
b. pitot pressure.
c. a pitot and a static source.
d. pitot, static and density.

15. The deflection of the pointer of the Airspeed Indicator is proportional to:
a. dynamic pressure.
b. static pressure.
c. the difference between static and dynamic pressure.
d. static pressure plus dynamic pressure.

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2 Questions 2 Questions

16. Calibration of the Airspeed Indicator is based upon the density:
a. at the altitude at which the aircraft is flying.
b. at sea level ICAO International Standard Atmosphere temperature.
c. at sea level.
d. at sea level ICAO International Standard Atmosphere +15°C temperature.

17. When considering the relationship between different types of airspeed:
1 - True Airspeed (TAS) is read directly from the Airspeed Indicator.
2 - Equivalent Airspeed is Indicated Airspeed corrected for position error.
3 - Indicated Airspeed is not a speed at all, it is a pressure.
4 - True Airspeed is the speed of the aircraft through the air.
Which of the above statements are true?

a. 1 only.
b. 2 and 3.
c. 3 and 4.
d. 1 and 4.
18. When considering the relationship between different types of Airspeed:
1 - Calibrated Airspeed is Indicated Airspeed corrected for position error.
2 - E quivalent Airspeed is Indicated Airspeed corrected for position error &

compressibility.
3 - Position error, which causes false Indicated Airspeed readings, is due to

variations in the pressures sensed at the pitot and static ports.
4 - The Airspeed Indicator is calibrated to read True Airspeed when the ambient

density is that of the ICAO International Standard Atmosphere at sea level.
The combination of correct statements is:

a. none of the statements are correct.
b. 1, 2 and 4.
c. 2 and 3.
d. 1, 2, 3 and 4.
19. The speed of sound:
a. is dependent upon the True Airspeed and the Mach number of the aircraft.
b. is inversely proportional to the absolute temperature.
c. is proportional to the square root of the absolute temperature of the air.
d. is directly proportional to the True Airspeed of the aircraft.
20. Mach number is:
a. the aircraft True Airspeed divided by the local speed of sound.
b. the speed of sound in the ambient conditions in which the aircraft is flying.
c. the True Airspeed of the aircraft at which the relative airflow somewhere on

the aircraft first reaches the local speed of sound.
d. the Indicated Airspeed divided by the local speed of sound sea level.

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2Questions Questions 2

21. An aircraft’s critical Mach number is:
a. the speed of the airflow when the aircraft first becomes supersonic.
b. the speed of the aircraft when the airflow somewhere reaches the speed of
sound.
c. the Indicated Airspeed when the aircraft first becomes supersonic.
d. the aircraft’s Mach number when airflow over it first reaches the local speed
of sound.

39

2 Answers 2 Answers

Answers

1 2 3 4 5 6 7 8 9 10 11 12
dbaba add c bd c
13 14 15 16 17 18 19 20 21
b c ab c d c ad

40

3Chapter

Basic Aerodynamic Theory

The Principle of Continuity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Bernoulli’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Streamlines and the Streamtube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

41

3 Basic Aerodynamic Theory 3 Basic AerodynamicTheory

42

3Basic AerodynamicTheory

The Principle of Continuity

One of the fundamental laws of the universe is ENERGY and MASS can neither be created Basic Aerodynamic Theory 3
nor destroyed, only changed from one form to another. To demonstrate the effect this basic
Principle of Continuity has on aerodynamic theory, it is instructive to consider a streamline
flow of air through a tube which has a reduced cross-sectional area in the middle.

The air mass flow, or mass per unit time, through the tube will be the product of the cross-
sectional area (A), the airflow velocity (V) and the air density (ρ). Mass flow will remain a
constant value at all points along the tube. The Equation of Continuity is:

A × V × ρ = Constant

Because air is a compressible fluid, any pressure change in the flow will affect the air density.
However, at low subsonic speeds (< M 0.4) density changes will be insignificant and can be
disregarded. The equation of continuity can now be simplified to: A × V = constant, or:

Velocity (V) = Constant
Area (A)

Airflow

Cross-sectional 1 m3 ½ m3 1 m3
Area (A) 52 m/s (100 kt) 104 m/s (200 kt) 52 m/s (100 kt)

Velocity (V) 52 m3/s 52 m3/s 52 m3/s

Mass Flow
(Constant)

Figure 3.1 The principle of continuity

Because the mass flow must remain constant, it can be seen from the equation of continuity
that the reduction in the tube’s cross-sectional area results in an increase in velocity, and vice
versa.

The equation of continuity enables the velocity changes of airflow around a given shape to be
predicted mathematically, (< M 0.4).

43

3 Basic Aerodynamic Theory 3 Basic AerodynamicTheory

Bernoulli’s Theorem

“In the steady flow of an ideal fluid the sum of the pressure energy and the kinetic energy
remains constant”.
Note: An ideal fluid is both incompressible and has no viscosity.
This statement can be expressed as: Pressure + Kinetic energy = Constant or:

p + 1/2 ρ V2 = Constant
Consider a mass of air: Static Pressure 101 325 N/m2, Density 1.225 kg/m3 and Velocity 52 m/s,
its dynamic pressure will be: 1656 N/m2. [Q = ½ × 1.225 × 52 × 52]
Pressure (101 325 N/m2 ) + Kinetic energy (1656 N/m2 ) = Constant (102 981 N/m2 )

Figure 3.2 Bernoulli’s Theorem

Because the velocity of air at the throat has doubled, its dynamic pressure has risen by a value
of four, and the static pressure has decreased. The significant point is that:
Static Pressure + Dynamic Pressure is a constant. This constant can be referred to either as:

TOTAL PRESSURE, STAGNATION PRESSURE or PITOT PRESSURE.
It can be seen that flow velocity is dependent on the shape of the object over which it flows.
And from Bernoulli’s theorem, it is evident that an increase in velocity will cause a decrease in
static pressure, and vice versa.

44